Sensing an opportunity to shut down the nominating contest, Obama campaign advisers said that they were orchestrating an endorsement of Mr. Obama by at least eight Senate and House members who had pledged to remain uncommitted until the primaries ended, and that the endorsements would come the moment the South Dakota polls closed on Tuesday night.

The group will be led by Senator Tom Harkin of Iowa, who on Monday met with three other uncommitted Democratic senators — Ken Salazar of Colorado, Thomas R. Carper of Delaware and Benjamin L. Cardin of Maryland — at the offices of the Democratic Senatorial Campaign Committee in what Mr. Salazar called a unity session.

Representative James E. Clyburn of South Carolina, the No. 3 Democrat in the House and the highest-ranking African-American in Congress, set his formal endorsement of Mr. Obama for Tuesday, and he was urging others to do the same. Other lawmakers and party insiders were also sending word that they would be falling in line behind Mr. Obama beginning as early as Tuesday morning.

“It’s time,” said Senator Herb Kohl of Wisconsin, one of the senators who have not made a public choice in the race, signaling that he too would announce his endorsement within days.